A quasi-static equivalent circuit model of a dumbbell shaped defected ground structure (DGS) is developed. The equivalent circuit model is derived from the equivalent inductance and capacitance developed due to the perturbed returned current path on the ground and the narrow gap, respectively. The theory is validated against the commercial full-wave solver CST Microwave Studio. Finally, the calculated results are compared with the measured results. Good agreement between the theory, the commercially available numerical analyses and the experimental results validates the developed theoretical model.